The Red Devils literally wore down a determined Everton side in a second half of almost constant pressure on the visitors' goal.
Yet again it was Cristiano Ronaldo who proved United's hero with both goals - the second a dramatic penalty two minutes from the end of normal time.
Ronaldo, the only one of United's first team to miss that infamous Christmas party this week, put to one side the disappointment of losing out on both major individual international football awards of the year to turn in another virtuoso performance for his side.
Ronaldo's opening goal in the 22nd minute was a piece of magnificent individual skill.
Collecting Carlos Tevez's pass to the right corner of the Everton box, the Portuguese winger sold the perfect dummy to Lee Carsley before crashing home a curling left-foot shot.
But United's lead was to last only five minutes.
Joleon Lescott played the ball to Steven Pienaar on the left and his deep cross to the far post saw Tim Cahill rise above Patrice Evra to head home from eight yards.
United piled on the pressure after the break and Everton finally cracked in the 88th minute.
Racing into the Everton box, Ryan Giggs was upended by Pienaar when he shaped to go on the outside of the South African.
Referee Howard Webb pointed to the spot and Ronaldo stepped up to coolly slot the ball right footed into the right corner of the net as Everton goalkeeper Tim Howard guessed wrong.
It was Ronaldo's 15th goal of the season and the fifth time he has scored twice in a game, but it was team-mate Tevez who was the star of the show.
He created chances all afternoon and harried Everton's defence for 90 minutes.
Tevez found Howard a worthy adversary on several occasions with the best of the American's saves a one-handed stop to keep out his 57th minute shot following an excellent one-two with Wayne Rooney.
If effort had been rewarded by goals then former Evertonian Rooney would certainly have been on the scoresheet.
He went close on a number of occasions, the closest being in the 33rd minute.
Giggs found Rooney on the left of the Everton penalty area and his audacious chip beat Howard only to be cleared off the line by Lescott's header.